The present invention relates to preparation, amendment and execution of a numerical simulation program, and more particularly to an information output method and device suitable for indicating the nature of simultaneous linear equations constructed by discretization equations which are approximation equations of a partial differential equation representing a physical phenomenon, and for indicating amendment of a mesh point of the partial differential equation.
A physical phenomenon can be represented by a partial differential equation representing a physical quantity, a boundary condition thereof, and an analysis domain which is a definition domain thereof.
In order to simulate the physical phenomenon on a computer, simultaneous linear equations are constructed by discretization equations which are approximation equations of field equations partial differential equation and boundary condition, and they are solved in the analysis domain.
A common approximation calculation method is shown in FIGS. 2, 3 and 4. In an analysis domain 21 shown in FIG. 2, a partial differential equation 22 and a boundary condition 23 are presented. An unknown quantity U 24 is to be determined by approximation calculation. As shown by 32 in FIG. 3, the analysis domain 21 is represented by a finite number of points P.sub.0 -P.sub.9 in the domain. Those points are called mesh points. A field equation (partial differential equation 22 or boundary condition 23) at each of the mesh points is discretized. In the discretization, a domain dependent quantity in the field equation is approximated by a relationship between the corresponding mesh point and the adjacent mesh points, and it is substituted by a linear equation between the mesh points. The adjacent mesh points are called discretization reference points (broken lines connecting the mesh points in the domain 32 of FIG. 3 represent relation of reference of the discretization), and the approximation equation derived from the discretization is called a discretization equation. For example, the discretization equation at the mesh point P2 shown by 33 in FIG. 3 is an equation 34 having unknowns U at the mesh point P2 and the discretization reference points P0, P1, P3 and P4. In the equation 34, U.sub.P0, U.sub.P1, U.sub.P2, U.sub.P3 and U.sub.P4 denote unknowns representing the quantities U at the respective mesh points, a-e denote coefficients for U's and con 2 denotes a constant. The discretization equation is defined at each of the mesh points P.sub.0 -P.sub.9, and the simultaneous linear equations constructed by all discretization equations (FIG. 4) are solved to obtain approximation solutions of U's.
The method for solving the partial differential equation to simulate a physical amount and automatically generating, by a computer, a program therefor based on input domain shape information and the partial differential equation has been referred to by, for example, Proc. of Fall Joint Computer Conference (1986), pp 1026-1033 and Denshi Tokyo, No. 25 (1986) pp 50-53. A related invention is disclosed in U.S. patent application Ser. No. 900,424 (filed Aug. 26, 1986) assigned to the assignee of the present invention.
In such approximation calculation, a numerical error may occur in the course of calculation or a resulting solution may not be correct. Then, an operator takes steps to investigate a cause of error. In one step, whether or not a coefficient matrix 41 and a constant matrix 42 of the simultaneous linear equations (FIG. 4) constructed by the discretization equations have valid values and valid tends is checked. The purposes therefor are twofold. One of the purposes is to check whether the meaning of the partial differential equation is precisely approximated and reflected by the discretization equation, that is, whether the discretization equation is correct or not. The second purpose is to check the nature of the coefficient matrix itself to determine whether the resulting matrix is suitable for a matrix solution method.
Finally, two examples of devices for checking the coefficients of the simultaneous linear equations are explained. It is assumed that a solution of the approximation calculation diverges. The coefficient matrix thereof is checked. It is assumed that it is found that, in the discretization equations in a partial domain of the analysis domain, an absolute value of a coefficient at a discretization reference point located in a specific direction is much larger than the absolute values of other coefficients. The operator thus modifies the discretization method for that partial domain. Furthermore, it is assumed that a numerical error occurs during matrix solution in the course of approximation calculation. From the coefficient matrix thereof, it is seen that a coefficient in the discretization equation for the mesh point Pn is zero. For example, when a discretization equation is generated for the mesh point P.sub.2 in 33 of FIG. 3, the coefficient of P.sub.2 is zero. In this case, an iterative matrix solution method (such as a biconjugate gradient method) is not applicable. The operator recognizes the occurrence of numerical error at the mesh point Pn and takes countermeasures. In checking the coefficient matrix and the constant matrix, the numeric data may be outputted on a display terminal. A position on the analysis domain of the discretization equation which has caused error may be manually identified by the mesh point number or coordinate values. The operator may add a number of mesh points around the mesh point at which the error has occurred, or may modify the discretization equation.
In the prior art method, when the operator checks the coefficient matrix and the constant matrix of the simultaneous linear equations constructed by the discretization equations, numerical data are outputted. For example, an analysis domain of a three-dimensional cubic is divided by ten in each of x, y and z directions, and crosspoints thereof are used as the mesh points (1,331 mesh points). For each mesh points, six mesh points located in shortest distance in plus or minus x, y and z directions are used as discretization reference points. Thus, the number of coefficients and constants amounts to more than tens of thousands. It is laborious to output such numerical data on sheets and manually examine it.
In the prior art method, the coefficient matrix and the coordinates of the mesh points are separately managed. Consequently, even if the cause of an error is found in a discretization equation of the simultaneous linear equations, it is difficult to determine a corresponding point on the analysis domain.
Because of these two points, the prior art method imparts burdens to the operator and is apt to generate an error.